Walkthrough
Prerequisite packages
Before we start the MetaboVariation walkthrough, the user should have working R software enviroment installed on their machine. The MetaboVaraiton package has following dependencies and will also be installed along with the package if not already installed on the machine.
- brms
- circlize
- ComplexHeatmap
- doParallel
- dplyr
- foreach
- future
- grid
- magrittr
- parallel
- plotly
- reshape2
- rstan
- scales
- stringr
- readxl
- tidyr
- ggplot2
Example data
“metabol.data” is a dataset that mimics the real life situation of how metabolomic data are stored in most cases. It is randomly created dataset that contains metabolites levels of 3 metabolites for 164 individuals taken on four different timepoints. Sex, Age and BMI are also recorded for these individuals in the data.
Some data preprocessing is also done on the data such as the “Subject_id” and “SexM.1F.2” are transformed to factor columns. THe names of covariates column and subject_id are stored in a variable for further use.
data(metabol.data)
colnames(metabol.data)
#> [1] "Individual_id" "SexM.1F.2" "Age" "BMI"
#> [5] "metabolA_1" "metabolA_2" "metabolA_3" "metabolA_4"
#> [9] "metabolB_1" "metabolB_2" "metabolB_3" "metabolB_4"
#> [13] "metabolC_1" "metabolC_2" "metabolC_3" "metabolC_4"
metabol.data$Individual_id = as.factor(metabol.data$Individual_id)
metabol.data$SexM.1F.2 = as.factor(metabol.data$SexM.1F.2)
covariates = c("SexM.1F.2","Age","BMI")
individual_id = "Individual_id"Extract metabolites name from the data
To extract a list of unique metabolites that are present in the data, the package has a function “get.metabolites” could be used to perform the task. It will read the list of column names that contains metabolite values and will provide a list of metabolite names after removing the timepoint infor from the column names. For correct result, the user should not pass any unnecessary column(any column that contains a covariate or subject_id information) to the function. The function will return a list containing the names of unique metabolites.
metabolite_list = colnames(metabol.data)[5:length(colnames(metabol.data))]
metabolites = get.metabolites(list = metabolite_list)
metabolites
#> [1] "metabolA" "metabolB" "metabolC"Get an understanding of the distribution of metabolites
To understand the distribution of the metabolite across timepoint before analysis, user can use the function “plotMetabolite”. The function plots the distribution of the metabolite for each timepoint as a violin plot. The user can pass a single or multiple metabolite to the function to get plots for every metabolite passed.
plotMetabolite(data = metabol.data,metabolite = metabolites[1:2])
#> Warning: Ignoring 34 observations
#> Warning: Ignoring 34 observationsThe user can set points=TRUE to get observations along the end of tail of the violin plots.
plotMetabolite(data = metabol.data,metabolite = metabolites[1],points = TRUE)
#> Warning: Ignoring 34 observationsModelling the data to get flagged individuals
The main function “MetaboVariation” performs the modelling. The fitting of the model and the predicting both happens in this function itself The function needs the data along with the names of covariates column (if any) and subject id column to understand data. It can work with single metabolite value or multiple values of metabolites.
# save_brms_model = FALSE It will not save the bayesian model developed
# during processing.
# full_posterior = FALSE It will not save the whole predicted posterior
# distribution that we got during predicting stage.
model = MetaboVariation(data = metabol.data, individual_ids = individual_id,
metabolite = metabolites[1:3],covariates = covariates,
save_brms_model = FALSE,full_posterior = FALSE)# full_posterior
#> Compiling Stan program...
#> Start sampling
#> Compiling Stan program...
#> Start sampling
#> Compiling Stan program...
#> Start samplingWhen multiple metabolites are passed to the function, it contains results for every metabolite as a list while each metabolite contains the following values.
- significant_covariates
- result
- warmup
- iterations
- Rhat
- metabolite
- full_posterior(optional output)
See ?MetaboVariation for further details about the function.
class(model)
#> [1] "MetaboVariation" "meta.multi_model"
names(model)
#> [1] "metabolA" "metabolB" "metabolC"class(model$metabolA)
#> [1] "MetaboVariation" "meta.single_model"
names(model$metabolA)
#> [1] "metabolite" "significant_covariates" "result"
#> [4] "warmup" "iterations" "Rhat"model$metabolA
#> $metabolite
#> [1] "metabolA"
#>
#> $significant_covariates
#> NULL
#>
#> $result
#> mean 2.5% 97.5% QR original identifier
#> 142 metabolA_1 469.1390 324.9673 609.2433 284.2759 594 1
#> 164 metabolA_1 302.4027 153.0321 445.2817 292.2496 355 1
#> 19 metabolA_1 395.6297 249.1008 544.9298 295.8290 445 1
#> 36 metabolA_1 293.7344 150.9293 437.3057 286.3763 321 1
#> 125 metabolA_1 369.6729 224.1535 516.1995 292.0460 534 0
#> 127 metabolA_1 390.8334 246.6101 536.3914 289.7814 360 1
#> 43 metabolA_1 348.4962 205.8424 492.1026 286.2602 243 1
#> 154 metabolA_1 437.5315 293.7106 583.3266 289.6160 469 1
#> 126 metabolA_1 362.9095 217.6067 504.6272 287.0205 378 1
#> 65 metabolA_1 354.8019 213.4763 495.6246 282.1482 405 1
#> 71 metabolA_1 378.0003 233.8162 521.6009 287.7847 297 1
#> 156 metabolA_1 374.0225 233.2649 520.7370 287.4721 315 1
#> 102 metabolA_1 377.2403 236.8405 520.1951 283.3545 335 1
#> 63 metabolA_1 317.8054 170.9983 461.9190 290.9207 347 1
#> 95 metabolA_1 337.6147 192.8829 480.4742 287.5913 394 1
#> 4 metabolA_1 346.7986 197.9256 493.6852 295.7596 289 1
#> 62 metabolA_1 301.4234 153.7483 444.6196 290.8713 253 1
#> 158 metabolA_1 499.2977 352.5173 640.3528 287.8355 573 1
#> 87 metabolA_1 457.3984 314.1359 598.0253 283.8893 363 1
#> 13 metabolA_1 397.8275 253.9759 543.9034 289.9276 322 1
#> 41 metabolA_1 387.2238 243.3284 525.9908 282.6624 312 1
#> 115 metabolA_1 345.4854 191.1411 494.7735 303.6324 374 1
#> 34 metabolA_1 357.4154 211.5314 499.5415 288.0102 435 1
#> 155 metabolA_1 366.6409 225.5896 513.6385 288.0489 351 1
#> 162 metabolA_1 373.5593 230.8501 513.0320 282.1819 423 1
#> 3 metabolA_1 380.2180 231.2636 522.9447 291.6811 382 1
#> 90 metabolA_1 318.2965 168.8834 459.7766 290.8933 347 1
#> 56 metabolA_1 367.2247 231.0240 507.7363 276.7123 321 1
#> 91 metabolA_1 368.8786 222.0678 517.1448 295.0770 347 1
#> 100 metabolA_1 377.0801 228.2959 519.4347 291.1388 352 1
#> 73 metabolA_1 338.3674 194.6251 484.2773 289.6522 279 1
#> 116 metabolA_1 321.7580 172.3828 458.4584 286.0755 291 1
#> 94 metabolA_1 341.4550 199.4707 487.2421 287.7714 344 1
#> 58 metabolA_1 361.5530 222.5986 505.0509 282.4523 358 1
#> 83 metabolA_1 317.4283 172.4657 460.3812 287.9155 296 1
#> 17 metabolA_1 355.7920 214.2374 496.6270 282.3896 346 1
#> 40 metabolA_1 392.2214 245.8594 544.2217 298.3623 509 1
#> 107 metabolA_1 402.4495 260.7990 543.9112 283.1122 465 1
#> 85 metabolA_1 379.2170 236.0066 523.0462 287.0396 499 1
#> 113 metabolA_1 336.6331 191.5213 480.8902 289.3688 230 1
#> 133 metabolA_1 317.9020 170.3555 461.5952 291.2397 386 1
#> 160 metabolA_1 383.6555 241.1656 527.4981 286.3325 385 1
#> 39 metabolA_1 272.4571 129.2762 411.6397 282.3635 210 1
#> 50 metabolA_1 340.4540 199.0477 485.9544 286.9067 336 1
#> 93 metabolA_1 376.6699 231.2023 522.9066 291.7043 292 1
#> 99 metabolA_1 356.4057 210.2264 497.9200 287.6936 273 1
#> 77 metabolA_1 374.5511 235.0213 515.0328 280.0115 387 1
#> 101 metabolA_1 272.5717 129.4118 415.3038 285.8920 249 1
#> 86 metabolA_1 372.8811 231.2155 519.8354 288.6199 361 1
#> 60 metabolA_1 326.3381 179.9114 473.2055 293.2941 305 1
#> 163 metabolA_1 342.5093 198.3888 488.0547 289.6660 332 1
#> 70 metabolA_1 401.6029 255.3301 550.9253 295.5951 533 1
#> 22 metabolA_1 314.4544 169.4032 460.0624 290.6592 299 1
#> 37 metabolA_1 318.4782 171.7014 464.4098 292.7084 276 1
#> 28 metabolA_1 336.8843 189.7048 482.1792 292.4745 345 1
#> 151 metabolA_1 346.0649 197.6513 488.1155 290.4642 362 1
#> 104 metabolA_1 312.3953 163.3434 457.3148 293.9714 297 1
#> 6 metabolA_1 317.2731 175.3052 457.0665 281.7613 277 1
#> 124 metabolA_1 365.8183 218.2377 511.9683 293.7305 358 1
#> 96 metabolA_1 349.5205 198.0002 494.6965 296.6963 302 1
#> 20 metabolA_1 322.2367 183.9243 469.7181 285.7938 348 1
#> 59 metabolA_1 313.4070 166.7320 460.7066 293.9746 260 1
#> 76 metabolA_1 436.6005 295.6435 582.3188 286.6753 514 1
#> 74 metabolA_1 336.3037 188.1911 474.7564 286.5653 366 1
#> 15 metabolA_1 390.8863 245.1791 537.5259 292.3468 267 1
#> 161 metabolA_1 412.3091 260.6434 557.2311 296.5877 394 1
#> 159 metabolA_1 335.6076 192.5213 475.9994 283.4780 295 1
#> 52 metabolA_1 406.5239 249.5189 552.3698 302.8508 504 1
#> 33 metabolA_1 327.5506 183.5519 473.2969 289.7451 336 1
#> 66 metabolA_1 373.6248 226.8421 516.4296 289.5875 300 1
#> 84 metabolA_1 347.1654 194.7245 496.9774 302.2529 360 1
#> 89 metabolA_1 405.2118 257.6561 553.9483 296.2922 374 1
#> 2 metabolA_1 326.1205 183.6951 471.2556 287.5605 266 1
#> 27 metabolA_1 368.5974 217.9452 522.4849 304.5397 412 1
#> 105 metabolA_1 343.7942 195.2762 496.0050 300.7287 318 1
#> 45 metabolA_1 353.5161 204.9711 500.1106 295.1394 453 1
#> 144 metabolA_1 381.0009 230.7733 533.5132 302.7400 404 1
#> 117 metabolA_1 315.9906 170.8141 457.0435 286.2295 293 1
#> 103 metabolA_1 404.2265 262.0689 549.1409 287.0720 483 1
#> 12 metabolA_1 321.6274 169.9848 469.0248 299.0400 321 1
#> 128 metabolA_1 344.7244 202.2138 493.1883 290.9745 384 1
#> 136 metabolA_1 354.2799 210.3515 498.7285 288.3770 332 1
#> 61 metabolA_1 362.7975 218.9740 502.9234 283.9494 270 1
#> 112 metabolA_1 362.1729 222.4396 507.8008 285.3611 401 1
#> 26 metabolA_1 328.9731 187.5456 474.8045 287.2589 317 1
#> 32 metabolA_1 315.9419 172.7439 460.5856 287.8417 266 1
#> 131 metabolA_1 428.0467 280.1213 575.1540 295.0327 269 0
#> 24 metabolA_1 353.9202 211.2718 499.1274 287.8557 363 1
#> 16 metabolA_1 377.8297 231.5656 523.2530 291.6874 341 1
#> 67 metabolA_1 339.9599 197.6205 485.5050 287.8845 434 1
#> 120 metabolA_1 303.9070 163.8343 452.4731 288.6388 277 1
#> 132 metabolA_1 420.5943 272.6184 561.0341 288.4157 350 1
#> 98 metabolA_1 354.8762 211.7110 500.6916 288.9806 391 1
#> 75 metabolA_1 440.0120 294.9463 583.9934 289.0471 442 1
#> 119 metabolA_1 410.4836 262.6797 556.1961 293.5164 455 1
#> 78 metabolA_1 413.7495 271.7904 556.7503 284.9599 422 1
#> 69 metabolA_1 424.7936 276.9252 568.9121 291.9869 518 1
#> 88 metabolA_1 383.6274 233.5544 531.1004 297.5460 454 1
#> 47 metabolA_1 324.2114 183.1169 467.1234 284.0065 292 1
#> 25 metabolA_1 373.2725 228.5172 514.2769 285.7597 424 1
#> 23 metabolA_1 398.7346 247.1437 553.6311 306.4874 568 0
#> 80 metabolA_1 313.9934 172.4694 457.6381 285.1686 303 1
#> 143 metabolA_1 319.7236 175.8652 462.8857 287.0205 283 1
#> 35 metabolA_1 439.5262 299.6187 585.1003 285.4817 487 1
#> 139 metabolA_1 369.8806 223.2354 510.7527 287.5173 359 1
#> 42 metabolA_1 290.0806 138.1012 438.1666 300.0654 235 1
#> 54 metabolA_1 338.9716 193.4307 483.9688 290.5381 415 1
#> 118 metabolA_1 397.3650 253.5264 541.1618 287.6354 684 0
#> 153 metabolA_1 423.3348 283.1145 568.7298 285.6153 300 1
#> 31 metabolA_1 338.3721 190.3345 488.0184 297.6839 406 1
#> 81 metabolA_1 391.5585 240.2659 534.3507 294.0848 401 1
#> 53 metabolA_1 348.9496 207.3747 488.6188 281.2441 446 1
#> 38 metabolA_1 376.5731 234.2107 520.9528 286.7421 298 1
#> 21 metabolA_1 314.7939 167.3275 458.9708 291.6433 272 1
#> 145 metabolA_1 356.3411 210.2649 505.2790 295.0142 290 1
#> 30 metabolA_1 378.8307 231.9548 523.7853 291.8304 405 1
#> 108 metabolA_1 351.8631 210.9269 498.2258 287.2989 413 1
#> 141 metabolA_1 335.0833 191.8397 479.0736 287.2339 309 1
#> 135 metabolA_1 309.7309 162.0941 456.2343 294.1401 318 1
#> 18 metabolA_1 360.1123 216.6665 498.0775 281.4110 395 1
#> 152 metabolA_1 368.7282 231.7935 508.8506 277.0572 531 0
#> 55 metabolA_1 358.0426 218.9966 500.2145 281.2179 337 1
#> 11 metabolA_1 328.5830 181.4383 478.3845 296.9463 272 1
#> 64 metabolA_1 416.3032 273.8652 562.2450 288.3798 406 1
#> 121 metabolA_1 421.5944 274.7270 564.5078 289.7808 507 1
#> 106 metabolA_1 414.4577 271.6898 560.1831 288.4934 510 1
#> 51 metabolA_1 360.9339 214.3594 503.3847 289.0252 237 1
#> 1 metabolA_1 278.8346 132.4846 417.6612 285.1766 278 1
#> 130 metabolA_1 343.9183 194.6887 489.6331 294.9444 311 1
#> 111 metabolA_1 300.2752 156.5719 443.1159 286.5440 276 1
#> 10 metabolA_1 391.2294 246.3956 534.2738 287.8782 432 1
#> 138 metabolA_1 381.1136 240.7400 522.0753 281.3354 499 1
#> 68 metabolA_1 369.7777 223.0087 521.4241 298.4155 339 1
#> 146 metabolA_1 315.0384 168.4334 459.1310 290.6975 268 1
#> 129 metabolA_1 321.8575 172.5007 467.6339 295.1333 291 1
#> 44 metabolA_1 339.2269 194.9731 478.5520 283.5789 309 1
#> 82 metabolA_1 431.2436 288.5541 575.4126 286.8585 464 1
#> 110 metabolA_1 363.6889 225.5253 504.5674 279.0421 270 1
#> 49 metabolA_1 355.4779 211.6277 501.2582 289.6305 385 1
#> 8 metabolA_1 331.6797 188.2701 473.3979 285.1278 219 1
#> 57 metabolA_1 384.7281 243.7658 527.6599 283.8941 351 1
#> 92 metabolA_1 401.1796 256.8156 547.6805 290.8649 320 1
#> 72 metabolA_1 360.3933 213.4370 503.5402 290.1032 303 1
#> 46 metabolA_1 346.3106 201.9327 492.9606 291.0279 310 1
#> 150 metabolA_1 432.6813 288.0618 578.0350 289.9732 445 1
#> 5 metabolA_1 256.2223 113.8068 403.9097 290.1029 212 1
#> 149 metabolA_1 408.6305 269.7143 552.7508 283.0365 266 0
#> 7 metabolA_1 270.4701 127.8686 418.3835 290.5149 278 1
#> 148 metabolA_1 317.6284 176.0637 461.3985 285.3348 334 1
#> 123 metabolA_1 360.0152 211.1984 500.5658 289.3674 452 1
#> 109 metabolA_1 319.5492 170.7109 463.8182 293.1072 266 1
#> 9 metabolA_1 376.5206 231.5671 518.2104 286.6433 389 1
#> 134 metabolA_1 400.4536 250.4010 549.1545 298.7535 521 1
#> 114 metabolA_1 278.3251 132.6726 425.9582 293.2856 257 1
#> 14 metabolA_1 358.2437 218.3666 498.2644 279.8979 357 1
#> 147 metabolA_1 321.5110 176.4377 461.8744 285.4368 302 1
#> 122 metabolA_1 293.5422 149.6022 441.1119 291.5096 230 1
#> 157 metabolA_1 453.9004 312.1636 596.4324 284.2688 531 1
#> 48 metabolA_1 376.2354 234.4256 516.3178 281.8922 314 1
#> 79 metabolA_1 298.9147 154.6362 441.4582 286.8221 279 1
#> 140 metabolA_1 357.3455 212.7324 503.4130 290.6806 454 1
#> 137 metabolA_1 434.5923 286.4117 582.6378 296.2261 500 1
#> 97 metabolA_1 391.7837 247.0050 532.9101 285.9051 388 1
#> 29 metabolA_1 388.4906 246.9552 534.0171 287.0620 401 1
#> 142 metabolA_2 469.0014 324.5843 611.6887 287.1044 500 1
#> 164 metabolA_2 301.7027 156.1711 448.9635 292.7924 243 1
#> 19 metabolA_2 393.9876 248.6130 540.7586 292.1455 391 1
#> 36 metabolA_2 292.6661 145.9787 441.8976 295.9190 223 1
#> 125 metabolA_2 368.4821 224.7801 511.4257 286.6456 337 1
#> 127 metabolA_2 391.2812 248.3306 535.1499 286.8193 456 1
#> 43 metabolA_2 350.9370 206.4193 494.6376 288.2184 368 1
#> 154 metabolA_2 437.2266 289.5896 586.2654 296.6758 437 1
#> 126 metabolA_2 362.7538 218.1379 504.9765 286.8386 317 1
#> 65 metabolA_2 356.0858 215.2773 502.1556 286.8783 379 1
#> 71 metabolA_2 377.4726 234.4584 519.0568 284.5984 363 1
#> 156 metabolA_2 371.8727 225.8464 518.2343 292.3880 313 1
#> 102 metabolA_2 377.3485 232.8610 519.1669 286.3059 334 1
#> 63 metabolA_2 318.3468 176.4116 467.1629 290.7513 246 1
#> 95 metabolA_2 334.6026 189.1659 476.4093 287.2435 301 1
#> 4 metabolA_2 345.8657 206.5349 501.9594 295.4245 461 1
#> 62 metabolA_2 302.0637 157.8954 448.2627 290.3672 305 1
#> 158 metabolA_2 499.0586 360.1856 639.5011 279.3155 449 1
#> 87 metabolA_2 458.6339 311.2412 600.5974 289.3562 475 1
#> 13 metabolA_2 399.7056 256.9374 545.1686 288.2312 503 1
#> 41 metabolA_2 387.1525 239.5416 531.8215 292.2799 284 1
#> 115 metabolA_2 346.8997 196.6999 496.9595 300.2596 308 1
#> 34 metabolA_2 358.0124 214.5113 505.8843 291.3730 402 1
#> 155 metabolA_2 365.7468 223.4827 508.5422 285.0595 294 1
#> 162 metabolA_2 372.4949 226.3756 512.9147 286.5391 380 1
#> 3 metabolA_2 382.3964 236.5500 523.9016 287.3517 289 1
#> 90 metabolA_2 314.9336 172.2015 456.0427 283.8412 269 1
#> 56 metabolA_2 366.7699 222.7978 510.2294 287.4316 455 1
#> 91 metabolA_2 369.4085 221.1017 518.8926 297.7909 353 1
#> 100 metabolA_2 379.2155 229.6274 522.9573 293.3299 411 1
#> 73 metabolA_2 339.8357 192.2683 484.5287 292.2604 309 1
#> 116 metabolA_2 320.8324 174.5244 465.2644 290.7400 286 1
#> 94 metabolA_2 343.6257 199.3991 484.2448 284.8458 360 1
#> 58 metabolA_2 363.7981 211.1182 505.1178 293.9996 305 1
#> 83 metabolA_2 319.9168 180.9041 468.3285 287.4244 306 1
#> 17 metabolA_2 352.3533 210.7347 495.4775 284.7427 410 1
#> 40 metabolA_2 390.5835 245.7935 535.9803 290.1868 311 1
#> 107 metabolA_2 403.0879 260.9542 552.4121 291.4579 481 1
#> 85 metabolA_2 380.8422 238.1996 528.5379 290.3384 312 1
#> 113 metabolA_2 337.5065 193.2747 484.6841 291.4094 344 1
#> 133 metabolA_2 319.0671 171.6062 462.6163 291.0101 213 1
#> 160 metabolA_2 382.9939 239.5969 529.1475 289.5506 384 1
#> 39 metabolA_2 270.7446 126.6660 410.5171 283.8511 276 1
#> 50 metabolA_2 339.6494 197.8089 482.9999 285.1910 343 1
#> 93 metabolA_2 375.5077 232.8372 523.2839 290.4467 313 1
#> 99 metabolA_2 358.4293 209.0726 504.0524 294.9798 402 1
#> 77 metabolA_2 375.8450 231.1670 522.1516 290.9845 452 1
#> 101 metabolA_2 272.2675 127.8791 415.7771 287.8980 262 1
#> 86 metabolA_2 372.4445 231.4229 518.2959 286.8730 345 1
#> 60 metabolA_2 325.5082 176.6962 470.1328 293.4366 305 1
#> 163 metabolA_2 345.7230 204.8175 488.6498 283.8322 334 1
#> 70 metabolA_2 403.2090 252.6210 547.6622 295.0412 394 1
#> 22 metabolA_2 315.9924 172.5616 462.9515 290.3898 304 1
#> 37 metabolA_2 318.1880 177.2279 463.5996 286.3717 241 1
#> 28 metabolA_2 337.8850 198.5810 482.7108 284.1298 292 1
#> 151 metabolA_2 345.3271 205.2393 491.0808 285.8415 343 1
#> 104 metabolA_2 313.7926 176.4322 456.7086 280.2764 244 1
#> 6 metabolA_2 320.1470 172.9322 463.1542 290.2221 343 1
#> 124 metabolA_2 369.0802 223.2002 513.6764 290.4762 417 1
#> 96 metabolA_2 350.8890 205.3854 496.1640 290.7785 485 1
#> 20 metabolA_2 322.0975 175.2704 465.4263 290.1559 308 1
#> 59 metabolA_2 312.1804 167.9984 458.0970 290.0987 303 1
#> 76 metabolA_2 434.5379 287.4395 579.9571 292.5176 470 1
#> 74 metabolA_2 335.9139 191.4362 481.1047 289.6684 318 1
#> 15 metabolA_2 390.0443 243.0838 536.7566 293.6728 522 1
#> 161 metabolA_2 413.4275 270.8291 560.7468 289.9177 462 1
#> 159 metabolA_2 334.5986 188.1693 475.9888 287.8195 346 1
#> 52 metabolA_2 403.7187 251.9873 556.0375 304.0502 360 1
#> 33 metabolA_2 326.6098 188.0103 471.1626 283.1523 252 1
#> 66 metabolA_2 371.8469 228.0092 516.5836 288.5744 469 1
#> 84 metabolA_2 346.2322 199.5350 499.3043 299.7693 314 1
#> 89 metabolA_2 402.8797 256.6952 549.3279 292.6327 308 1
#> 2 metabolA_2 325.6164 184.5311 469.7590 285.2278 287 1
#> 27 metabolA_2 370.7688 223.0296 524.0611 301.0315 358 1
#> 105 metabolA_2 343.1874 191.9618 494.8122 302.8504 339 1
#> 45 metabolA_2 356.6188 214.0946 497.0066 282.9120 320 1
#> 144 metabolA_2 381.8731 233.3274 529.1884 295.8609 405 1
#> 117 metabolA_2 316.1986 170.7905 465.6002 294.8097 308 1
#> 103 metabolA_2 405.3651 258.2017 546.8185 288.6168 337 1
#> 12 metabolA_2 323.8389 170.5508 472.2238 301.6730 275 1
#> 128 metabolA_2 345.4856 200.2691 492.1122 291.8431 324 1
#> 136 metabolA_2 354.1403 210.3720 501.9797 291.6077 457 1
#> 61 metabolA_2 362.8270 217.7997 511.3703 293.5707 367 1
#> 112 metabolA_2 362.3197 224.6997 504.9414 280.2418 295 1
#> 26 metabolA_2 327.6118 181.7058 473.2313 291.5254 325 1
#> 32 metabolA_2 317.8057 171.8510 463.3394 291.4884 286 1
#> 131 metabolA_2 428.4110 286.0816 573.5060 287.4244 585 0
#> 24 metabolA_2 354.8781 212.6932 496.6999 284.0067 303 1
#> 16 metabolA_2 379.2528 230.6875 519.3102 288.6227 367 1
#> 67 metabolA_2 340.0631 200.5578 485.2879 284.7300 306 1
#> 120 metabolA_2 305.5230 160.4233 450.1077 289.6844 329 1
#> 132 metabolA_2 420.6215 274.0408 563.1820 289.1412 401 1
#> 98 metabolA_2 352.9946 204.1780 497.8141 293.6361 299 1
#> 75 metabolA_2 435.3578 288.8100 583.3469 294.5369 510 1
#> 119 metabolA_2 410.3958 263.2273 557.5914 294.3641 491 1
#> 78 metabolA_2 409.5589 267.3397 553.4408 286.1011 422 1
#> 69 metabolA_2 424.8496 287.6207 567.0951 279.4745 412 1
#> 88 metabolA_2 384.4041 235.1408 539.3042 304.1634 386 1
#> 47 metabolA_2 324.3125 180.0307 467.3045 287.2738 315 1
#> 25 metabolA_2 371.5136 226.7408 519.8750 293.1342 415 1
#> 23 metabolA_2 398.4895 248.7492 546.6369 297.8877 279 1
#> 80 metabolA_2 315.3278 167.7300 457.2643 289.5343 286 1
#> 143 metabolA_2 321.2356 176.9345 463.9072 286.9726 314 1
#> 35 metabolA_2 436.4312 284.1195 582.4001 298.2806 538 1
#> 139 metabolA_2 370.1251 228.5297 518.7223 290.1926 400 1
#> 42 metabolA_2 288.7147 139.0632 439.8116 300.7484 228 1
#> 54 metabolA_2 342.1437 198.9944 487.0527 288.0583 300 1
#> 118 metabolA_2 397.1114 250.7973 544.2586 293.4612 243 0
#> 153 metabolA_2 421.8540 280.3111 567.1901 286.8791 469 1
#> 31 metabolA_2 338.7849 196.4921 479.7541 283.2620 256 1
#> 81 metabolA_2 390.6068 247.1022 536.2138 289.1115 379 1
#> 53 metabolA_2 348.7377 206.0686 490.7508 284.6822 320 1
#> 38 metabolA_2 378.5696 236.1902 525.9313 289.7411 398 1
#> 21 metabolA_2 312.5196 160.9496 456.1384 295.1889 352 1
#> 145 metabolA_2 355.6339 206.0798 505.5522 299.4724 397 1
#> 30 metabolA_2 379.2139 234.3832 530.5666 296.1834 373 1
#> 108 metabolA_2 353.9594 205.8934 499.9238 294.0305 313 1
#> 141 metabolA_2 335.9609 194.7214 477.2011 282.4797 417 1
#> 135 metabolA_2 310.9997 165.0163 456.9611 291.9448 317 1
#> 18 metabolA_2 361.1938 220.3114 506.9156 286.6041 302 1
#> 152 metabolA_2 370.3304 220.0251 515.1531 295.1281 342 1
#> 55 metabolA_2 356.6926 215.4295 499.3499 283.9204 372 1
#> 11 metabolA_2 330.4373 185.6934 475.2810 289.5876 257 1
#> 64 metabolA_2 417.2826 275.8020 564.3369 288.5349 501 1
#> 121 metabolA_2 421.0374 276.9247 562.8298 285.9051 376 1
#> 106 metabolA_2 415.6915 269.9209 562.8557 292.9348 349 1
#> 51 metabolA_2 362.5363 217.0209 504.2582 287.2373 394 1
#> 1 metabolA_2 280.0742 136.3559 428.3235 291.9676 208 1
#> 130 metabolA_2 343.5381 202.1929 483.2562 281.0633 359 1
#> 111 metabolA_2 300.5764 155.0223 444.2321 289.2098 232 1
#> 10 metabolA_2 390.7096 253.4609 532.4383 278.9774 403 1
#> 138 metabolA_2 379.4923 238.6576 520.6210 281.9634 280 1
#> 68 metabolA_2 373.7186 230.3536 519.6484 289.2948 382 1
#> 146 metabolA_2 313.6196 174.1897 455.8942 281.7045 298 1
#> 129 metabolA_2 322.6142 178.8454 471.1429 292.2976 369 1
#> 44 metabolA_2 337.7999 192.1679 484.0236 291.8557 338 1
#> 82 metabolA_2 432.4584 291.8390 575.2489 283.4100 474 1
#> 110 metabolA_2 365.1067 223.0879 506.7615 283.6736 447 1
#> 49 metabolA_2 356.7972 209.6944 500.7317 291.0373 355 1
#> 8 metabolA_2 333.0550 187.3062 474.2285 286.9223 483 0
#> 57 metabolA_2 385.0771 243.6053 531.2766 287.6713 436 1
#> 92 metabolA_2 398.7487 256.6731 543.7260 287.0529 418 1
#> 72 metabolA_2 360.8536 209.3772 511.0864 301.7093 456 1
#> 46 metabolA_2 345.3621 201.7781 491.8097 290.0316 393 1
#> 150 metabolA_2 433.3053 286.5100 577.8889 291.3790 326 1
#> 5 metabolA_2 256.5473 117.0559 406.8792 289.8233 186 1
#> 149 metabolA_2 409.9541 268.8613 554.1596 285.2983 368 1
#> 7 metabolA_2 270.3545 127.1615 415.6643 288.5028 212 1
#> 148 metabolA_2 317.7497 173.4183 460.3292 286.9109 240 1
#> 123 metabolA_2 361.4897 223.7273 500.8560 277.1288 320 1
#> 109 metabolA_2 319.3940 176.0078 458.7454 282.7377 327 1
#> 9 metabolA_2 375.7377 229.2505 516.1276 286.8771 360 1
#> 134 metabolA_2 401.1317 247.1666 550.9737 303.8070 360 1
#> 114 metabolA_2 280.2192 139.6441 421.3066 281.6625 273 1
#> 14 metabolA_2 358.8270 215.1062 508.9049 293.7987 341 1
#> 147 metabolA_2 321.1578 175.1071 463.3325 288.2253 229 1
#> 122 metabolA_2 292.0235 139.3224 439.2301 299.9076 273 1
#> 157 metabolA_2 456.1483 309.7561 599.4065 289.6504 494 1
#> 48 metabolA_2 377.6234 234.4332 518.3304 283.8972 280 1
#> 79 metabolA_2 297.8816 151.5577 444.9355 293.3777 282 1
#> 140 metabolA_2 356.8051 212.1233 497.5026 285.3793 310 1
#> 137 metabolA_2 436.9069 290.5743 580.7989 290.2246 484 1
#> 97 metabolA_2 390.6775 245.1809 533.7687 288.5879 409 1
#> 29 metabolA_2 390.5774 245.7443 534.3830 288.6387 423 1
#> 142 metabolA_3 467.8626 322.9317 617.6220 294.6903 444 1
#> 164 metabolA_3 300.7663 154.9172 449.6240 294.7068 267 1
#> 19 metabolA_3 396.7423 252.4982 543.2536 290.7554 451 1
#> 36 metabolA_3 292.9389 151.1864 436.9823 285.7959 292 1
#> 125 metabolA_3 368.2773 223.6070 510.4177 286.8107 313 1
#> 127 metabolA_3 389.4803 245.8786 531.5328 285.6542 427 1
#> 43 metabolA_3 350.2500 208.0007 491.8240 283.8234 360 1
#> 154 metabolA_3 437.1616 296.2318 579.6400 283.4082 521 1
#> 126 metabolA_3 363.7896 216.4580 505.5454 289.0874 423 1
#> 65 metabolA_3 353.5351 208.8848 496.8169 287.9321 263 1
#> 71 metabolA_3 377.4281 236.6831 520.1091 283.4260 424 1
#> 156 metabolA_3 375.2125 224.9484 523.3024 298.3540 366 1
#> 102 metabolA_3 377.1612 232.2457 523.2479 291.0022 452 1
#> 63 metabolA_3 320.4781 174.5249 465.4959 290.9710 277 1
#> 95 metabolA_3 337.5195 195.8030 481.7530 285.9500 268 1
#> 4 metabolA_3 348.0332 199.8509 492.3723 292.5214 308 1
#> 62 metabolA_3 299.0806 150.8969 443.8065 292.9095 330 1
#> 158 metabolA_3 496.9695 350.3515 640.3703 290.0188 708 0
#> 87 metabolA_3 457.3127 309.7315 600.0827 290.3512 588 1
#> 13 metabolA_3 401.9096 254.7152 547.3208 292.6056 434 1
#> 41 metabolA_3 387.7380 243.1565 531.3400 288.1835 414 1
#> 34 metabolA_3 356.5565 213.8251 497.9087 284.0836 329 1
#> 155 metabolA_3 366.3759 225.1443 510.6458 285.5015 367 1
#> 162 metabolA_3 372.5489 227.4422 512.9493 285.5070 413 1
#> 90 metabolA_3 315.8845 170.8542 460.2152 289.3611 326 1
#> 56 metabolA_3 366.9157 224.4092 517.5206 293.1114 303 1
#> 91 metabolA_3 366.8145 229.7865 508.5648 278.7783 407 1
#> 100 metabolA_3 380.0559 234.9258 525.1842 290.2585 391 1
#> 73 metabolA_3 339.2712 192.8489 479.7019 286.8529 344 1
#> 116 metabolA_3 320.6042 171.0095 469.2803 298.2708 315 1
#> 94 metabolA_3 342.9073 200.5491 487.8515 287.3024 361 1
#> 58 metabolA_3 366.0805 223.2100 511.9783 288.7683 421 1
#> 83 metabolA_3 318.4610 178.2651 459.6731 281.4080 301 1
#> 17 metabolA_3 354.2273 204.1527 502.6090 298.4562 282 1
#> 40 metabolA_3 389.5997 240.1599 537.6123 297.4524 414 1
#> 107 metabolA_3 402.3485 259.6704 543.1319 283.4616 386 1
#> 85 metabolA_3 379.9831 235.1606 527.6551 292.4945 369 1
#> 113 metabolA_3 336.2734 192.3193 485.2252 292.9058 479 1
#> 133 metabolA_3 316.7635 169.6162 461.5728 291.9566 374 1
#> 160 metabolA_3 383.3675 242.7619 527.2639 284.5020 396 1
#> 39 metabolA_3 271.4492 132.3969 416.9637 284.5668 202 1
#> 50 metabolA_3 342.3832 199.6729 489.1689 289.4960 307 1
#> 93 metabolA_3 376.6630 230.0242 519.3777 289.3535 417 1
#> 77 metabolA_3 374.4543 229.9230 518.0726 288.1496 361 1
#> 101 metabolA_3 272.7789 129.2250 417.7541 288.5291 214 1
#> 86 metabolA_3 374.0373 226.3931 515.4173 289.0241 353 1
#> 60 metabolA_3 326.4425 174.9599 476.7819 301.8220 307 1
#> 163 metabolA_3 343.3380 196.6277 487.9208 291.2931 325 1
#> 70 metabolA_3 404.1017 256.2202 548.0198 291.7996 399 1
#> 22 metabolA_3 314.2044 170.0947 460.5325 290.4378 263 1
#> 37 metabolA_3 320.3712 175.3932 460.6495 285.2563 399 1
#> 28 metabolA_3 336.2398 197.3516 480.3789 283.0274 267 1
#> 151 metabolA_3 342.9919 201.1286 488.7061 287.5776 305 1
#> 104 metabolA_3 311.3961 171.8196 456.9721 285.1525 322 1
#> 6 metabolA_3 317.6524 171.9422 464.6208 292.6786 286 1
#> 124 metabolA_3 368.8105 223.8633 512.0907 288.2273 343 1
#> 96 metabolA_3 351.9471 205.4066 497.2398 291.8333 339 1
#> 20 metabolA_3 321.6456 174.5102 467.0999 292.5897 257 1
#> 59 metabolA_3 310.1044 168.8982 453.8673 284.9691 360 1
#> 76 metabolA_3 433.5760 287.2359 577.8221 290.5862 495 1
#> 74 metabolA_3 336.6155 189.1421 482.1552 293.0131 347 1
#> 15 metabolA_3 391.6708 246.1750 539.0928 292.9178 446 1
#> 161 metabolA_3 411.4646 262.4721 559.6344 297.1623 459 1
#> 159 metabolA_3 337.7408 194.5473 481.2139 286.6666 380 1
#> 33 metabolA_3 327.1962 184.7331 468.7079 283.9748 312 1
#> 66 metabolA_3 373.8349 231.2202 521.6754 290.4552 374 1
#> 2 metabolA_3 325.8952 183.7017 470.6078 286.9060 368 1
#> 45 metabolA_3 354.3045 209.9586 499.6599 289.7013 297 1
#> 117 metabolA_3 315.9478 173.3635 461.8547 288.4912 305 1
#> 103 metabolA_3 403.9162 257.3210 547.1463 289.8252 373 1
#> 128 metabolA_3 343.5067 195.8030 487.1773 291.3743 367 1
#> 136 metabolA_3 354.4606 215.8394 499.0575 283.2180 333 1
#> 61 metabolA_3 362.0227 219.8630 507.9741 288.1110 450 1
#> 112 metabolA_3 362.3954 218.3656 502.4285 284.0629 401 1
#> 26 metabolA_3 328.1132 183.8523 475.0946 291.2423 333 1
#> 32 metabolA_3 318.6622 171.7813 455.3992 283.6179 326 1
#> 131 metabolA_3 426.6904 282.2633 569.1352 286.8720 465 1
#> 24 metabolA_3 352.3171 212.1992 495.3539 283.1547 345 1
#> 16 metabolA_3 378.2758 233.5848 522.1494 288.5646 394 1
#> 67 metabolA_3 338.7814 197.4537 483.3600 285.9063 257 1
#> 120 metabolA_3 307.1534 163.7282 457.5310 293.8028 316 1
#> 132 metabolA_3 421.9823 279.9913 564.6446 284.6534 425 1
#> 98 metabolA_3 355.1026 211.2818 498.0152 286.7335 387 1
#> 75 metabolA_3 436.8388 296.5263 578.1235 281.5972 479 1
#> 119 metabolA_3 409.9680 262.0286 554.4147 292.3861 370 1
#> 78 metabolA_3 411.6538 265.1091 557.3683 292.2592 484 1
#> 69 metabolA_3 424.3057 282.3543 566.9679 284.6136 360 1
#> 88 metabolA_3 384.6509 232.6072 529.0995 296.4924 358 1
#> 47 metabolA_3 324.8635 185.2773 470.8128 285.5355 310 1
#> 25 metabolA_3 373.7254 231.3056 512.8379 281.5323 363 1
#> 80 metabolA_3 315.3121 170.6198 460.6416 290.0218 367 1
#> 143 metabolA_3 321.2563 174.9612 463.3205 288.3593 236 1
#> 35 metabolA_3 438.2712 290.8430 585.9861 295.1431 429 1
#> 139 metabolA_3 369.1776 219.4613 509.9530 290.4917 347 1
#> 54 metabolA_3 340.7270 201.2837 482.9466 281.6629 328 1
#> 118 metabolA_3 398.6791 252.8225 543.3086 290.4861 311 1
#> 153 metabolA_3 424.5774 278.9506 565.4368 286.4862 434 1
#> 31 metabolA_3 338.0885 188.7925 483.3602 294.5677 354 1
#> 81 metabolA_3 390.8830 242.0464 535.8322 293.7858 415 1
#> 53 metabolA_3 348.9487 208.1105 493.3375 285.2269 332 1
#> 38 metabolA_3 376.9462 234.2820 518.5212 284.2392 459 1
#> 21 metabolA_3 314.5699 167.5580 458.3476 290.7896 275 1
#> 30 metabolA_3 380.7769 231.5084 532.7973 301.2890 377 1
#> 108 metabolA_3 355.2528 209.9617 501.5204 291.5587 416 1
#> 141 metabolA_3 334.4539 189.7181 478.7617 289.0436 337 1
#> 135 metabolA_3 308.6788 167.7530 456.7364 288.9834 241 1
#> 18 metabolA_3 359.6794 218.7327 501.9452 283.2125 301 1
#> 152 metabolA_3 369.3828 225.0083 513.4453 288.4369 319 1
#> 55 metabolA_3 356.5790 214.9514 501.2784 286.3270 392 1
#> 11 metabolA_3 329.5452 183.5464 478.7696 295.2231 406 1
#> 64 metabolA_3 418.3755 272.8210 566.6392 293.8182 427 1
#> 121 metabolA_3 420.9270 273.0191 563.5682 290.5492 473 1
#> 106 metabolA_3 416.1011 275.0244 561.1082 286.0838 531 1
#> 51 metabolA_3 360.4577 207.4467 504.8528 297.4060 466 1
#> 1 metabolA_3 281.5760 133.2341 428.0845 294.8504 227 1
#> 130 metabolA_3 343.4668 201.0873 481.2425 280.1552 371 1
#> 111 metabolA_3 300.3224 155.9029 442.2465 286.3436 312 1
#> 10 metabolA_3 391.3006 251.2919 538.7834 287.4915 429 1
#> 138 metabolA_3 378.9511 232.4580 522.9479 290.4899 409 1
#> 68 metabolA_3 373.2495 228.0511 515.9224 287.8713 316 1
#> 146 metabolA_3 314.4467 167.5244 458.3747 290.8503 282 1
#> 129 metabolA_3 321.7049 178.7991 461.7850 282.9859 254 1
#> 44 metabolA_3 336.3664 191.7212 482.7914 291.0703 369 1
#> 82 metabolA_3 431.0375 284.1169 576.6524 292.5355 444 1
#> 110 metabolA_3 362.7318 215.7881 505.5363 289.7482 397 1
#> 49 metabolA_3 355.5102 211.6401 495.3506 283.7105 346 1
#> 8 metabolA_3 332.7538 184.4742 477.1752 292.7010 313 1
#> 57 metabolA_3 387.4343 246.9379 530.1583 283.2204 487 1
#> 92 metabolA_3 401.2165 253.0883 545.8168 292.7286 613 0
#> 72 metabolA_3 360.5086 215.8607 502.8534 286.9927 327 1
#> 46 metabolA_3 344.5988 199.5275 484.4247 284.8972 342 1
#> 150 metabolA_3 435.5387 291.9690 580.2322 288.2632 478 1
#> 5 metabolA_3 255.0084 113.1748 398.4036 285.2288 184 1
#> 149 metabolA_3 409.8463 264.4734 555.6110 291.1376 561 0
#> 7 metabolA_3 270.9362 127.8169 418.2101 290.3932 236 1
#> 148 metabolA_3 319.8007 175.8116 465.8374 290.0258 308 1
#> 123 metabolA_3 358.4615 214.0064 496.6653 282.6589 314 1
#> 109 metabolA_3 316.7683 172.3169 458.3554 286.0384 299 1
#> 9 metabolA_3 375.1745 229.5615 516.0671 286.5056 396 1
#> 114 metabolA_3 279.5289 136.3621 423.7604 287.3983 214 1
#> 14 metabolA_3 360.8907 215.3765 505.2816 289.9050 373 1
#> 147 metabolA_3 321.8373 176.5731 462.4728 285.8997 386 1
#> 122 metabolA_3 294.8944 151.7105 442.6764 290.9659 234 1
#> 157 metabolA_3 454.6192 310.5317 601.3214 290.7897 488 1
#> 48 metabolA_3 378.5483 240.7577 517.0338 276.2761 632 0
#> 79 metabolA_3 296.5191 149.9812 438.2231 288.2419 242 1
#> 140 metabolA_3 357.6497 211.7439 500.8859 289.1420 329 1
#> 137 metabolA_3 437.5070 287.6201 579.1987 291.5786 408 1
#> 97 metabolA_3 390.7764 252.4364 534.0172 281.5808 397 1
#> 29 metabolA_3 387.4122 244.0656 536.1066 292.0411 330 1
#> 142 metabolA_4 466.9784 322.2117 613.7861 291.5744 535 1
#> 164 metabolA_4 301.8551 157.6030 449.6086 292.0057 255 1
#> 19 metabolA_4 393.3922 243.8634 544.4752 300.6118 360 1
#> 36 metabolA_4 293.4352 146.1872 431.7718 285.5845 221 1
#> 125 metabolA_4 369.5833 228.1625 513.6760 285.5135 322 1
#> 127 metabolA_4 391.5203 248.3027 541.7777 293.4749 348 1
#> 43 metabolA_4 348.7785 205.5212 493.8632 288.3420 418 1
#> 154 metabolA_4 437.3853 291.4881 584.1928 292.7047 434 1
#> 126 metabolA_4 363.5911 220.4019 507.2512 286.8493 339 1
#> 65 metabolA_4 354.2869 207.5316 493.3764 285.8448 338 1
#> 71 metabolA_4 377.5875 227.3850 527.9638 300.5788 438 1
#> 156 metabolA_4 373.0519 224.1136 521.3714 297.2578 524 0
#> 102 metabolA_4 376.7429 230.4719 520.3310 289.8592 407 1
#> 63 metabolA_4 319.0357 174.5261 465.6328 291.1067 327 1
#> 95 metabolA_4 335.3346 192.4399 476.2431 283.8032 342 1
#> 4 metabolA_4 345.7911 201.9910 490.1318 288.1408 308 1
#> 62 metabolA_4 300.9981 155.5861 440.0685 284.4824 216 1
#> 158 metabolA_4 499.9248 354.6229 643.4353 288.8124 521 1
#> 87 metabolA_4 457.1350 311.7346 606.5482 294.8135 558 1
#> 13 metabolA_4 400.7903 257.5501 546.5543 289.0042 410 1
#> 41 metabolA_4 388.0326 247.9494 527.0104 279.0610 574 0
#> 34 metabolA_4 357.1537 214.6737 498.2853 283.6116 265 1
#> 155 metabolA_4 365.1751 225.6990 507.3017 281.6027 469 1
#> 162 metabolA_4 375.2469 225.5069 521.4876 295.9807 313 1
#> 3 metabolA_4 380.6180 233.1445 526.2023 293.0578 493 1
#> 90 metabolA_4 316.3017 171.5182 460.3364 288.8182 262 1
#> 56 metabolA_4 366.4247 219.1019 507.5326 288.4306 418 1
#> 91 metabolA_4 367.5517 220.0239 515.2666 295.2427 394 1
#> 100 metabolA_4 379.8410 232.9333 524.0610 291.1277 407 1
#> 73 metabolA_4 336.5235 194.1602 478.5330 284.3728 354 1
#> 116 metabolA_4 321.3080 178.6854 461.3256 282.6401 332 1
#> 94 metabolA_4 342.6714 200.1471 487.2124 287.0653 294 1
#> 83 metabolA_4 318.4201 175.0911 469.5631 294.4720 310 1
#> 17 metabolA_4 355.9427 213.6555 498.3677 284.7121 361 1
#> 107 metabolA_4 401.3913 260.0302 540.9274 280.8972 360 1
#> 85 metabolA_4 381.3454 239.8856 525.4866 285.6010 366 1
#> 113 metabolA_4 336.6116 196.5665 480.1341 283.5676 260 1
#> 133 metabolA_4 315.6600 173.9245 455.5418 281.6172 225 1
#> 160 metabolA_4 382.3936 237.5648 525.5407 287.9759 373 1
#> 39 metabolA_4 273.6730 130.3064 414.4469 284.1405 247 1
#> 50 metabolA_4 340.3932 196.2952 484.3315 288.0362 338 1
#> 93 metabolA_4 375.1390 232.8484 521.8143 288.9660 524 0
#> 99 metabolA_4 358.7006 211.6229 507.3190 295.6961 402 1
#> 77 metabolA_4 375.1501 227.4839 521.2214 293.7374 297 1
#> 101 metabolA_4 273.3161 127.7223 414.6118 286.8895 209 1
#> 86 metabolA_4 373.3202 225.4220 514.7860 289.3639 454 1
#> 163 metabolA_4 341.7310 200.0780 486.2632 286.1851 359 1
#> 70 metabolA_4 403.8373 259.9986 545.0307 285.0320 358 1
#> 37 metabolA_4 316.8486 170.2966 465.2805 294.9839 274 1
#> 28 metabolA_4 334.5861 184.3490 476.4603 292.1113 395 1
#> 151 metabolA_4 344.3103 199.5961 489.2588 289.6627 338 1
#> 104 metabolA_4 311.0940 167.8715 457.8642 289.9927 302 1
#> 6 metabolA_4 318.2767 176.8343 461.4169 284.5826 305 1
#> 124 metabolA_4 366.7730 225.6580 512.5045 286.8465 340 1
#> 96 metabolA_4 350.4924 206.7471 495.5916 288.8444 261 1
#> 20 metabolA_4 321.6764 182.2173 461.8747 279.6574 307 1
#> 59 metabolA_4 310.1973 159.5363 456.3220 296.7857 246 1
#> 76 metabolA_4 435.1672 285.8344 582.2337 296.3993 379 1
#> 74 metabolA_4 336.0931 194.1580 484.0397 289.8817 279 1
#> 15 metabolA_4 390.7603 246.3457 535.1217 288.7761 365 1
#> 161 metabolA_4 413.9277 267.7985 557.3467 289.5482 444 1
#> 159 metabolA_4 335.5571 192.0560 478.8225 286.7665 282 1
#> 33 metabolA_4 328.6803 182.7589 474.8711 292.1122 330 1
#> 66 metabolA_4 373.0594 232.7717 517.6717 284.9001 369 1
#> 89 metabolA_4 404.5384 251.9303 554.8439 302.9136 618 0
#> 2 metabolA_4 326.3090 180.7177 471.9456 291.2279 340 1
#> 45 metabolA_4 354.1440 213.2225 497.0151 283.7926 347 1
#> 117 metabolA_4 316.8059 166.8256 457.6094 290.7838 264 1
#> 103 metabolA_4 405.8480 264.2288 547.8913 283.6626 514 1
#> 128 metabolA_4 341.9789 193.2761 487.5678 294.2918 267 1
#> 136 metabolA_4 353.4897 208.3433 501.0973 292.7541 266 1
#> 61 metabolA_4 363.4714 225.2636 502.9172 277.6536 380 1
#> 112 metabolA_4 362.3590 220.9254 501.0559 280.1305 340 1
#> 26 metabolA_4 329.1092 188.9249 469.3545 280.4296 271 1
#> 32 metabolA_4 316.0526 168.4600 460.1585 291.6985 330 1
#> 131 metabolA_4 428.0329 287.7163 568.5286 280.8123 505 1
#> 24 metabolA_4 352.2677 206.6570 495.8539 289.1970 390 1
#> 16 metabolA_4 378.4236 236.0574 520.8069 284.7495 424 1
#> 67 metabolA_4 339.9208 194.9315 485.9355 291.0040 311 1
#> 120 metabolA_4 304.7128 158.0395 453.1285 295.0889 220 1
#> 132 metabolA_4 418.3163 273.6776 557.8005 284.1228 623 0
#> 98 metabolA_4 354.4615 207.4525 501.0448 293.5923 330 1
#> 75 metabolA_4 437.5693 297.8389 578.3720 280.5330 459 1
#> 78 metabolA_4 412.8407 269.2919 556.0366 286.7447 426 1
#> 69 metabolA_4 424.2227 279.1874 564.8646 285.6772 500 1
#> 47 metabolA_4 327.0919 186.2421 467.3329 281.0908 337 1
#> 25 metabolA_4 370.8883 225.7443 512.8772 287.1329 292 1
#> 80 metabolA_4 315.9011 174.3287 457.4535 283.1248 239 1
#> 143 metabolA_4 320.5827 176.8827 465.1943 288.3116 375 1
#> 35 metabolA_4 437.3984 289.4925 578.3941 288.9016 438 1
#> 139 metabolA_4 367.8312 224.0277 514.2816 290.2539 374 1
#> 54 metabolA_4 340.6621 192.5847 482.0377 289.4529 288 1
#> 153 metabolA_4 424.3860 282.5366 573.7941 291.2575 585 0
#> 31 metabolA_4 338.4357 198.7985 482.1085 283.3099 308 1
#> 81 metabolA_4 390.6618 247.9275 537.0524 289.1249 426 1
#> 53 metabolA_4 349.6237 206.5489 491.9820 285.4331 292 1
#> 38 metabolA_4 377.0136 231.3472 519.0406 287.6934 389 1
#> 21 metabolA_4 313.9468 169.2930 459.6888 290.3958 277 1
#> 108 metabolA_4 351.6537 208.0306 495.7228 287.6921 271 1
#> 141 metabolA_4 334.0220 189.6459 480.6052 290.9593 227 1
#> 135 metabolA_4 310.5809 164.1549 455.0695 290.9146 276 1
#> 18 metabolA_4 361.5648 216.6105 505.9964 289.3859 462 1
#> 152 metabolA_4 370.1464 224.2379 509.0994 284.8615 311 1
#> 55 metabolA_4 356.7900 214.9400 503.9976 289.0576 336 1
#> 64 metabolA_4 416.2184 265.7302 559.6241 293.8938 448 1
#> 121 metabolA_4 420.7702 277.2517 564.3342 287.0825 412 1
#> 106 metabolA_4 415.1416 270.8737 560.9653 290.0916 360 1
#> 51 metabolA_4 360.5780 213.4803 505.0619 291.5816 336 1
#> 1 metabolA_4 278.9905 134.0469 421.4607 287.4138 267 1
#> 130 metabolA_4 342.5170 201.9328 488.0427 286.1098 310 1
#> 111 metabolA_4 301.0305 160.3725 447.7410 287.3685 287 1
#> 10 metabolA_4 391.6773 244.5043 534.7348 290.2305 372 1
#> 138 metabolA_4 381.1926 241.8582 519.8925 278.0343 364 1
#> 68 metabolA_4 373.9955 228.3780 518.9463 290.5683 455 1
#> 146 metabolA_4 314.5184 167.9328 462.2043 294.2714 340 1
#> 129 metabolA_4 321.8331 177.9540 464.2571 286.3031 296 1
#> 44 metabolA_4 337.1197 193.8679 480.9660 287.0981 315 1
#> 82 metabolA_4 429.4120 282.5002 574.1676 291.6673 442 1
#> 110 metabolA_4 362.2622 220.1210 505.1762 285.0552 352 1
#> 49 metabolA_4 358.1080 211.2864 506.1800 294.8936 345 1
#> 8 metabolA_4 332.4552 183.9474 478.7657 294.8184 276 1
#> 57 metabolA_4 386.6297 244.3923 533.3138 288.9216 323 1
#> 92 metabolA_4 399.3938 256.7195 547.1615 290.4421 314 1
#> 72 metabolA_4 360.1486 216.2821 503.3442 287.0621 374 1
#> 46 metabolA_4 346.5650 204.1410 491.5493 287.4083 322 1
#> 150 metabolA_4 434.1825 286.7434 577.8377 291.0943 596 0
#> 5 metabolA_4 255.4364 114.1363 399.1427 285.0064 270 1
#> 149 metabolA_4 411.1490 265.4936 552.1523 286.6587 515 1
#> 7 metabolA_4 270.0157 122.1862 412.1325 289.9463 209 1
#> 148 metabolA_4 318.7190 175.9967 459.2571 283.2604 329 1
#> 123 metabolA_4 359.0932 218.2127 505.2539 287.0412 361 1
#> 109 metabolA_4 316.7605 171.3100 460.7614 289.4515 297 1
#> 9 metabolA_4 376.4324 231.5268 520.0827 288.5559 391 1
#> 114 metabolA_4 279.9096 139.5788 427.8488 288.2700 220 1
#> 14 metabolA_4 359.2953 218.1020 506.5463 288.4443 378 1
#> 147 metabolA_4 320.2203 178.2108 463.4514 285.2406 307 1
#> 122 metabolA_4 293.5790 145.4370 438.0698 292.6328 308 1
#> 157 metabolA_4 457.1207 307.6012 606.0553 298.4542 487 1
#> 48 metabolA_4 378.5106 236.7656 519.7752 283.0096 327 1
#> 79 metabolA_4 297.6979 149.3545 442.9099 293.5554 269 1
#> 140 metabolA_4 358.4666 211.0754 501.0618 289.9864 324 1
#> 137 metabolA_4 435.7299 289.2236 580.6205 291.3969 472 1
#> 97 metabolA_4 392.9230 246.0012 537.6329 291.6317 417 1
#> 29 metabolA_4 389.6093 242.3459 535.2708 292.9250 463 1
#>
#> $warmup
#> [1] 1000
#>
#> $iterations
#> [1] 2000
#>
#> $Rhat
#> [1] 1.001121
#>
#> attr(,"class")
#> [1] "MetaboVariation" "meta.single_model"Plotting the results
After modelling, “plot” helps in visualization of the results. It can show the results in three format i.e. circos plot, number of individual counts per timepoint for each metabolite or metabolites count for each individual.
- “circos” plot will show 95% credible interval of predicted posterior distribution for all the timepoints and if the actual value is outside the interval, the individual will be flagged.
- “metabolites_count” plot will show how many individuals are flagged in each timepoint for every metablite present in the “MetaboVariation” object.
- “subject_count” plot will shows a heat map which shows how many time an individual have been flagged for each metabolite.
# type = "circos", "metabolites_count", "subject_count"
# timepoints = NULL/ vector Either all the timepoints are plotted in
# the plots or a list of numeric vectors are plotted in the plot
plot(x= model$metabolA,type = "circos",timepoints = NULL)
plot(x = model,type = "circos",timepoints = c(1,2,3))
plot(x = model, type = "metabolites_count",timepoints = c(1,2,3))Getting a list of flagged individuals from the results
After modelling, to get a list of individuals that have been flagged in single metabolite, you can use the function “flaggedIndividuals”. The function will give a list of individuals that have been flagged by the model and will provide covariate information and the metabolite levels for the all timepoints as well.
flaggedIndividuals(model$metabolA, data = metabol.data,
individual_id = individual_id, covariates=covariates)
#> Individual_id SexM.1F.2 Age BMI metabolA_1 metabolA_2 metabolA_3
#> 5 125 2 26 23.11188 534 337 313
#> 12 156 2 53 19.41610 315 313 366
#> 18 158 2 24 22.80810 573 449 708
#> 21 41 1 25 20.37293 312 284 414
#> 45 93 2 29 22.60840 292 313 417
#> 72 89 2 30 18.73433 374 308 NA
#> 87 131 2 57 17.29884 269 585 465
#> 92 132 2 20 19.94309 350 401 425
#> 101 23 1 30 22.57041 568 279 NA
#> 108 118 1 59 24.40705 684 243 311
#> 109 153 1 37 25.40170 300 469 434
#> 121 152 2 27 23.04124 531 342 319
#> 140 8 2 22 24.88852 219 483 313
#> 142 92 2 58 23.52960 320 418 613
#> 145 150 1 50 23.01478 445 326 478
#> 147 149 1 37 24.63512 266 368 561
#> 159 48 2 33 22.34531 314 280 632
#> metabolA_4
#> 5 322
#> 12 524
#> 18 521
#> 21 574
#> 45 524
#> 72 618
#> 87 505
#> 92 623
#> 101 NA
#> 108 NA
#> 109 585
#> 121 311
#> 140 276
#> 142 314
#> 145 596
#> 147 515
#> 159 327In case the model contains multiple metabolites, the function will return the list of individuals along with their covariates details. To get number of individuals that have been flagged in at least “n” metabolites, you can set the threshold to “n”.
flaggedIndividuals(model, data = metabol.data,
individual_id = individual_id, covariates=covariates, threshold = 1)
#> Individual_id SexM.1F.2 Age BMI
#> 5 125 2 26 23.11188
#> 12 156 2 53 19.41610
#> 13 102 1 26 20.82453
#> 18 158 2 24 22.80810
#> 21 41 1 25 20.37293
#> 23 34 2 29 21.49119
#> 27 90 2 18 26.84647
#> 36 17 1 21 20.95306
#> 38 107 2 28 26.97759
#> 44 50 2 59 22.94392
#> 45 93 2 29 22.60840
#> 63 76 1 25 22.95575
#> 67 159 2 43 25.32872
#> 68 52 1 44 29.99253
#> 70 66 2 57 28.82654
#> 72 89 2 30 18.73433
#> 75 105 2 56 21.47219
#> 83 61 2 25 22.41476
#> 87 131 2 57 17.29884
#> 92 132 2 20 19.94309
#> 95 119 2 48 25.76327
#> 99 47 2 32 23.69862
#> 101 23 1 30 22.57041
#> 103 143 1 26 25.37708
#> 104 35 2 56 26.26751
#> 108 118 1 59 24.40705
#> 109 153 1 37 25.40170
#> 110 31 2 34 18.20000
#> 116 30 1 46 23.99519
#> 121 152 2 27 23.04124
#> 123 11 2 46 28.94320
#> 132 138 2 49 23.90785
#> 140 8 2 22 24.88852
#> 142 92 2 58 23.52960
#> 145 150 1 50 23.01478
#> 147 149 1 37 24.63512
#> 148 7 2 28 20.62667
#> 151 109 1 24 22.43579
#> 159 48 2 33 22.34531